Introduction to Rational Functions

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4.10.1 Introduction to Rational Functions

An object of type RATFUN in CoCoA represents a rational function, i.e., a quotient of polynomials. Each rational function is represented as P/Q where P and Q are polynomials (of type POLY) and deg(Q) > 0. Common factors of the numerator and denominator are automatically simplified. At present, rational functions in CoCoA are only available over a field.

Example

  Use R ::= QQ[x,y];
  F := x/(x+y);  -- a rational function
  F*(x+y);
x
-------------------------------
  (x^2-y^2)/(x+y);  -- the result here is a polynomial
x - y
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The following algebraic operations on rational functions are supported:

  F^N, +F, -F, F*G, F/G, F+G, F-G,

where F, G are rational functions and N is an integer.

For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").